Chapter 17, Problem 1IR

To determine

To find:

The root of the givenradicalassuming that all variables represent nonnegative real numbers.

Answer to Problem 1IR

The root of the given radical is $9$ .

Explanation of Solution

Given:

A radical expression: $\sqrt{81}$ .

Calculation:

Let us find the root of the given radical using exponent properties as shown below:

  $\begin{array}{l}\sqrt{81}(\text{Given expression)}\\ \Rightarrow \sqrt{9\cdot 9}(\text{Factoring 81)}\\ \Rightarrow \sqrt{9^2}\\ \Rightarrow 9\left(\text{Applying rule }\sqrt[n]{a^n}=a\right)\end{array}$

Therefore, the root of our given radical is $9$ .